library(readr)
library(taRifx)
library(tidyr)
library(plotly)
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Attaching package: ‘plotly’

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FreeE_Propanediol.df <- read_table2("/home/aarcher/Downloads/FreeE_Propanediol.txt")
Parsed with column specification:
cols(
  `Axial-coord` = col_double(),
  `Radial-coord` = col_double(),
  freeE = col_double()
)
FreeE_Propanal.df <- read_table2("/home/aarcher/Downloads/FreeE_Propanal[2].txt")
Parsed with column specification:
cols(
  `Axial-coord` = col_double(),
  `Radial-coord` = col_double(),
  freeE = col_double()
)
FreeE_Propanediol.df <- FreeE_Propanediol.df[FreeE_Propanediol.df$`Axial-coord` > -9& FreeE_Propanediol.df$`Axial-coord` < 9,]
FreeE_Propanal.df <- FreeE_Propanal.df[FreeE_Propanal.df$`Axial-coord` > -9& FreeE_Propanal.df$`Axial-coord` < 9,]
FreeE_Propanediol_Center.df <- FreeE_Propanediol.df[FreeE_Propanediol.df$`Radial-coord` == 0.75 & FreeE_Propanediol.df$`Axial-coord` > -9& FreeE_Propanediol.df$`Axial-coord` < 9,]
FreeE_Propanal_Center.df <- FreeE_Propanal.df[FreeE_Propanal.df$`Radial-coord` == 0.75 & FreeE_Propanal.df$`Axial-coord` > -9& FreeE_Propanal.df$`Axial-coord` < 9,]
ggplot(data = FreeE_Propanediol.df, mapping = aes(x = `Radial-coord`, y = `Axial-coord`, fill = freeE)) + geom_tile() +  xlab(label = "Radius Coord")+  ylab(label = "Axial Coord") + ggtitle('Free Energy Distribution of 1,2-PDO')

plot(FreeE_Propanediol_Center.df$`Axial-coord`,FreeE_Propanediol_Center.df$freeE,ylab='Average Free Energy of 1,2-PDO', xlab='Axial Coord')

ggplot(data = FreeE_Propanal.df, mapping = aes(x = `Radial-coord`, y = `Axial-coord`, fill = freeE)) + geom_tile() +  xlab(label = "Radius Coord")+  ylab(label = "Axial Coord") + ggtitle('Free Energy Distribution of 1,2-PDO')

plot(FreeE_Propanal_Center.df$`Axial-coord`,FreeE_Propanal_Center.df$freeE,ylab='Average Free Energy of Proponal', xlab='Axial Coord')

corr <- function(tv1,tv2,eta1){
  K = matrix(1,nrow=dim(tv1)[1],ncol=dim(tv2)[1])
  for(dlcv in 1:dim(tv1)[2]){
  K <- K*exp(-eta1[dlcv]*outer(tv1[,dlcv],tv2[,dlcv],'-')^2)
  }
  K
}
MLE <-function(logeta, to, fo){
  m <- length(logeta)
  logeta1 <- logeta[-m]
  logeta2 <- logeta[m]
  
  # obtain the covariance via kronecker product
  
  corr0 <- corr(to, to, exp(logeta1))# c(., .)
  kappa0 <- corr0 + exp(logeta2)*diag(length(as.vector(fo)))
  kappa0_inv <- solve(kappa0)
  kappa0_inv_f0 <- solve(kappa0, as.vector(fo))
  kappa0_inv_1 <- solve(kappa0, rep(1, length(as.vector(fo))))# estimated values
  gammahat <- sum(kappa0_inv_f0)/sum(kappa0_inv_1)
  sigmahat <- mean(t(kappa0_inv_f0 - gammahat*kappa0_inv_1)*(as.vector(fo) - gammahat))
  return(list(gammahat=gammahat, sigmahat=sigmahat))
  }
# train each f as GP
negloglik <-function(logeta, t0, f0){
  n <- length(as.vector(f0))# obtain sigmahat for a given eta
  m <- length(logeta)
  logeta1 <- logeta[-m]
  logeta2 <- logeta[m]
  estimators <- MLE(logeta, t0, f0)
  sigmahat <- estimators$sigmahat# obtain the covariance matrices
  corr0 <- corr(t0, t0, exp(logeta1))# c(t0, t0)
  kappa0 <- corr0 + exp(logeta2)*diag(n)
  # obtain the log of determinants efficiently
  logdetkappa0 <- determinant(kappa0,logarithm=TRUE)$modulus
  return(1/2*logdetkappa0 + n/2*log(sigmahat))
  }
fitGP <-function(logeta=c(1, 1, 1), lowerb=c(-1, -1,-1), upperb=c(4, 4,4), t_tr, f_tr){
  log_eta_hat <- optim(par=logeta,fn=negloglik,lower=lowerb,upper=upperb,method="L-BFGS-B", t0=t_tr, f0=f_tr)$par
  estimators <- MLE(log_eta_hat, t_tr, f_tr)
  m <- length(log_eta_hat)
  return(list(etahat=exp(log_eta_hat[-m]),g=exp(log_eta_hat[m]),sigmahat=estimators$sigmahat,gammahat=estimators$gammahat))
}
predictGP <-function(fitted_info, t_test, t_tr, f_tr){# obtain the fitted info
  etahat1 <- fitted_info$etahat
  g <- fitted_info$g
  sigmahat <- fitted_info$sigmahat
  gammahat <- fitted_info$gammahat
  
  # obtain the final covariance structure
  
  corr0 <- corr(t_tr, t_tr, etahat1)  # c(t_tr, t_tr)
  kappa0 <- corr0 + g*diag(length(as.vector(f_tr)))
  kappa0_inv <- (1/sigmahat)*solve(kappa0)
  kappa0_inv_f0 <- kappa0_inv%*%(as.vector(f_tr) - gammahat)
  corr_Tv <- corr(t_test, t_tr, etahat1)# c(t_test, t_tr)
  kappa_Tv <- sigmahat*corr_Tv# c(t_test, t_tr)
  
  corr_toTv <- corr(t_tr, t_test, etahat1)# c(t_tr, t_test)
  kappa_toTv <- sigmahat *corr_toTv#  c(., .)
  
  gamma_vec <- (gammahat + kappa_Tv%*%kappa0_inv_f0)
  dkappa <- sigmahat * rep(1, dim(t_test)[1]*dim(f_tr)[2])
  kappa_vec <- (pmax(dkappa -apply(t((kappa_Tv)%*%(kappa0_inv))*(kappa_toTv), 2, sum), 10**(-13)))
  return(list(pred_mean=gamma_vec, pred_var=kappa_vec))}
ftrain <- as.matrix(FreeE_Propanal.df[,3])
inputtrain <-as.matrix(FreeE_Propanal.df[,1:2])
fitted_info <- fitGP(logeta=c(1, 1,1), lowerb=c(0, 0,0), upperb=c(5, 5,5), inputtrain, ftrain)
fitted_info
$etahat
[1] 1 1

$g
[1] 1

$sigmahat
[1] 2.181122

$gammahat
[1] 5.102003
predmean =rep(0,dim(inputtrain)[1])
predLB =  rep(0,dim(inputtrain)[1])
predUB =rep(0,dim(inputtrain)[1])
for(k in 1:dim(inputtrain)[1]){
  predinfo <- predictGP(fitted_info,t(as.matrix(inputtrain[k,])), inputtrain, ftrain)
  predmean[k] <- predinfo$pred_mean
  predLB[k] = predmean[k]- qnorm(1-0.05/2)*sqrt(predinfo$pred_var)
  predUB[k] = predmean[k]+ qnorm(1-0.05/2)*sqrt(predinfo$pred_var)
}
print(paste('PCGPMethod: Test MSE:',round(mean((predmean-ftrain)^2),3),', Coverage:',100*round(mean((predLB<ftrain)*(predUB>ftrain)),3),'%',sep =''))
[1] "PCGPMethod: Test MSE:0.764, Coverage:95.6%"
FreeE_Propanal_Pred.df <- FreeE_Propanal.df
FreeE_Propanal_LB.df <- FreeE_Propanal.df
FreeE_Propanal_UB.df <- FreeE_Propanal.df
FreeE_Propanal_Pred.df$freeE <- predmean
FreeE_Propanal_LB.df$freeE <- predLB
FreeE_Propanal_UB.df$freeE <- predUB
z <- as.matrix(spread(FreeE_Propanal.df, `Radial-coord`, freeE)[,-1])
zpred <- as.matrix(spread(FreeE_Propanal_Pred.df, `Radial-coord`, freeE)[,-1])
zLB <- as.matrix(spread(FreeE_Propanal_LB.df, `Radial-coord`, freeE)[,-1])
zUB <- as.matrix(spread(FreeE_Propanal_UB.df, `Radial-coord`, freeE)[,-1])
color <- rep(1, length(z))
dim(color) <- dim(z)
x <-unique(FreeE_Propanal.df$`Radial-coord`)
y <-unique(FreeE_Propanal.df$`Axial-coord`)
p<-  plot_ly() %>% add_trace(x=FreeE_Propanal.df$`Radial-coord`, y=FreeE_Propanal.df$`Axial-coord`, z=FreeE_Propanal.df$freeE, mode= "markers",type = "scatter3d",marker = list(size = 2, color = "blue", symbol = 104), opacity=0.7,showlegend = FALSE )
p <- p %>% add_trace( x=x, y=y, z=zpred,type = "surface",colorscale = list(c(0, 1), c("tan", "blue")),opacity=0.7)  
df1 <- split(FreeE_Propanal_LB.df, FreeE_Propanal_LB.df$`Radial-coord`)
df2 <- split(FreeE_Propanal_LB.df, FreeE_Propanal_LB.df$`Axial-coord`)
for(i in seq_along(df1)){
  df_sp <- df1[[i]]
  p <- add_trace(p, line = list(
    color = "#000000", 
    width = 2
  ), 
  mode = "lines", 
  type = "scatter3d", 
  x = df_sp$`Radial-coord`,
  y = df_sp$`Axial-coord`,
  z = df_sp$freeE,
  showlegend = FALSE)
}
for(i in seq_along(df2)){
  df_sp <- df2[[i]]
  p <- add_trace(p, line = list(
    color = "#000000", 
    width = 2
  ), 
  mode = "lines", 
  type = "scatter3d", 
  x = df_sp$`Radial-coord`,
  y = df_sp$`Axial-coord`,
  z = df_sp$freeE,
  showlegend = FALSE)
}
df1 <- split(FreeE_Propanal_UB.df, FreeE_Propanal_UB.df$`Radial-coord`)
df2 <- split(FreeE_Propanal_UB.df, FreeE_Propanal_UB.df$`Axial-coord`)
for(i in seq_along(df1)){
  df_sp <- df1[[i]]
  p <- add_trace(p, line = list(
    color = "#FF0000", 
    width = 2
  ), 
  mode = "lines", 
  type = "scatter3d", 
  x = df_sp$`Radial-coord`,
  y = df_sp$`Axial-coord`,
  z = df_sp$freeE,
  showlegend = FALSE)
}
for(i in seq_along(df2)){
  df_sp <- df2[[i]]
  p <- add_trace(p, line = list(
    color = "#FF0000", 
    width = 2
  ), 
  mode = "lines", 
  type = "scatter3d", 
  x = df_sp$`Radial-coord`,
  y = df_sp$`Axial-coord`,
  z = df_sp$freeE,
  showlegend = FALSE)
}
p%>% layout(scene = list( xaxis = list(title = "Radius, r"),yaxis = list(title = "Axial, z")))
axiallen <- 1000
axialcoord <- unique(FreeE_Propanal.df$`Axial-coord`)
centercoords <-as.matrix( data.frame(seq(min(axialcoord),max(axialcoord),length.out=axiallen),rep(0,axiallen)))
predmean =rep(0,dim(centercoords)[1])
predLB =  rep(0,dim(centercoords)[1])
predUB =rep(0,dim(centercoords)[1])
for(k in 1:dim(centercoords)[1]){
  predinfo <- predictGP(fitted_info,t(as.matrix(centercoords[k,])), inputtrain, ftrain)
  predmean[k] <- predinfo$pred_mean
  predLB[k] = predmean[k]- qnorm(1-0.05/2)*sqrt(predinfo$pred_var)
  predUB[k] = predmean[k]+ qnorm(1-0.05/2)*sqrt(predinfo$pred_var)
}
plot(centercoords[,1],predmean, ylim = c(min(predLB),max(predUB)))
lines(centercoords[,1],predLB)
lines(centercoords[,1],predUB)

deltax = (max(axialcoord)-min(axialcoord))/(axiallen-1)
predmeandev = (predmean[3:axiallen]-predmean[1:(axiallen-2)])/deltax
preddevLB = (predLB[3:axiallen]-predLB[1:(axiallen-2)])/deltax
preddevUB = (predUB[3:axiallen]-predUB[1:(axiallen-2)])/deltax
predmeandevdev = (predmean[3:axiallen]-2*predmean[2:(axiallen-1)] + predmean[1:(axiallen-2)])/deltax^2
preddevdevLB = (predLB[3:axiallen]-2*predmean[2:(axiallen-1)] +predLB[1:(axiallen-2)])/deltax^2
preddevdevUB = (predUB[3:axiallen]-2*predmean[2:(axiallen-1)] +predUB[1:(axiallen-2)])/deltax^2
indmean = which(predmean==max(predmean))
indLB = which(predLB==max(predLB))
indUB = which(predUB==max(predUB))
print(predmean[indmean])
[1] 5.922285
print(predLB[indLB])
[1] 3.288251
print(predUB[indUB])
[1] 8.559228
plot(centercoords[2:(axiallen-1),1],predmeandev , ylim = c(min(predmeandev,preddevLB,preddevUB),max(predmeandev,preddevLB,preddevUB)))
lines(centercoords[2:(axiallen-1),1],preddevLB)
lines(centercoords[2:(axiallen-1),1],preddevUB)

print(predmeandev[indmean])
[1] -0.01772556
print(preddevLB[indLB])
[1] -0.0243247
print(preddevUB[indUB])
[1] -0.01114983
plot(centercoords[2:(axiallen-1),1],predmeandevdev , ylim = c(min(predmeandevdev,preddevdevLB,preddevdevUB),max(predmeandevdev,preddevdevLB,preddevdevUB)))
lines(centercoords[2:(axiallen-1),1],preddevdevLB)
lines(centercoords[2:(axiallen-1),1],preddevdevUB)

print(predmeandevdev[indmean])
[1] -0.4683776
print(preddevdevLB[indLB])
[1] -18189.59
print(preddevdevUB[indUB])
[1] 18223.72
corrdevobv <- function(tv1,tv2,eta1){
  K <- -2*eta1[1]*exp(-eta1[1]*outer(tv1[,1],tv2[,1],'-')^2)*(outer(tv1[,1],tv2[,1],'-'))
  K <- K*exp(-eta1[2]*abs(outer(tv1[,2],tv2[,2],'-'))^2)
  K
}
predictGPdev <-function(fitted_info, t_test, t_tr, f_tr){# obtain the fitted info
  etahat1 <- fitted_info$etahat
  g <- fitted_info$g
  sigmahat <- fitted_info$sigmahat
  gammahat <- fitted_info$gammahat
  
  # obtain the final covariance structure
  
  corr0 <- corr(t_tr, t_tr, etahat1)  # c(t_tr, t_tr)
  kappa0 <- corr0 + g*diag(length(as.vector(f_tr)))
  kappa0_inv <- (1/sigmahat)*solve(kappa0)
  kappa0_inv_f0 <- kappa0_inv%*%(as.vector(f_tr) - gammahat)
  corr_Tv <- corrdevobv(t_test, t_tr, etahat1)# c(t_test, t_tr)
  kappa_Tv <- sigmahat*corr_Tv# c(t_test, t_tr)
  
  corr_toTv <- corrdevobv(t_tr, t_test, etahat1)# c(t_tr, t_test)
  kappa_toTv <- sigmahat *corr_toTv#  c(., .)
  
  gamma_vec <-  kappa_Tv%*%kappa0_inv_f0
  dkappa <- sigmahat*(1 + g)*rep(1, dim(t_test)[1]*dim(f_tr)[2])
  kappa_vec <- (pmax(dkappa -apply(t((kappa_Tv)%*%(kappa0_inv))*(kappa_toTv), 2, sum), 10**(-13)))
  return(list(pred_mean=gamma_vec, pred_var=kappa_vec))}
predmeandev =rep(0,dim(centercoords)[1])
predLBdev =  rep(0,dim(centercoords)[1])
predUBdev =rep(0,dim(centercoords)[1])
for(k in 1:dim(centercoords)[1]){
  predinfo <- predictGPdev(fitted_info,t(as.matrix(centercoords[k,])), inputtrain, ftrain)
  predmeandev[k] <- predinfo$pred_mean
  predLBdev[k] = predmeandev[k] - qnorm(1-0.05/2)*sqrt(predinfo$pred_var)
  predUBdev[k] = predmeandev[k]+ qnorm(1-0.05/2)*sqrt(predinfo$pred_var)
}
plot(centercoords[,1],predmeandev)# ylim = c(min(predLBdev),max(predUBdev)))
lines(centercoords[,1],predLBdev)
lines(centercoords[,1],predUBdev)

inds = which(diff(sign(predmeandev)) != 0)
print(predmeandev[inds])
[1] -0.0013450402  0.0007428134 -0.0036200835  0.0072476454 -0.0017144610
print(predLBdev[inds])
[1] -4.333562 -4.313164 -4.325467 -4.294252 -4.301100
print(predUBdev[inds])
[1] 4.330872 4.314650 4.318227 4.308747 4.297671
corrdevdevobv <- function(tv1,tv2,eta1){
  K <- 2*eta1[1]*exp(-eta1[1]*outer(tv1[,1],tv2[,1],'-')^2)*(2*eta1[1]*(outer(tv1[,1],tv2[,1],'-'))^2-1)
  K <- K*exp(-eta1[2]*abs(outer(tv1[,2],tv2[,2],'-'))^2)
  K
}
corrdevdevdevobv <- function(tv1,tv2,eta1){
  K <- -4*(eta1[1]^2)*(outer(tv1[,1],tv2[,1],'-'))*exp(-eta1[1]*outer(tv1[,1],tv2[,1],'-')^2)*(2*eta1[1]*(outer(tv1[,1],tv2[,1],'-'))^2-3)
  K <- K*exp(-eta1[2]*abs(outer(tv1[,2],tv2[,2],'-'))^2)
  K
}
corrdevdevdevdevobv <- function(tv1,tv2,eta1){
  K <- 4*(eta1[1]^2)*exp(-eta1[1]*outer(tv1[,1],tv2[,1],'-')^2)*(4*eta1[1]*(outer(tv1[,1],tv2[,1],'-')^2)*(eta1[1]*(outer(tv1[,1],tv2[,1],'-'))^2-3)+3)
  K <- K*exp(-eta1[2]*abs(outer(tv1[,2],tv2[,2],'-'))^2)
  K
}
predictGPdevdev <-function(fitted_info, t_test, t_tr, f_tr){# obtain the fitted info
  etahat1 <- fitted_info$etahat
  g <- fitted_info$g
  sigmahat <- fitted_info$sigmahat
  gammahat <- fitted_info$gammahat
  
  # obtain the final covariance structure
  
  corr0 <- corr(t_tr, t_tr, etahat1)  # c(t_tr, t_tr)
  kappa0 <- corr0 + g*diag(length(as.vector(f_tr)))
  kappa0_inv <- (1/sigmahat)*solve(kappa0)
  kappa0_inv_f0 <- kappa0_inv%*%(as.vector(f_tr) - gammahat)
  corr_Tv <- corrdevdevobv(t_test, t_tr, etahat1)# c(t_test, t_tr)
  kappa_Tv <- sigmahat*corr_Tv# c(t_test, t_tr)
  
  corr_toTv <- corrdevdevobv(t_tr, t_test, etahat1)# c(t_tr, t_test)
  kappa_toTv <- sigmahat *corr_toTv#  c(., .)
  
  gamma_vec <-  kappa_Tv%*%kappa0_inv_f0
  dkappa <- sigmahat*(1 + g)*rep(1, dim(t_test)[1]*dim(f_tr)[2])
  kappa_vec <- (pmax(dkappa -apply(t((kappa_Tv)%*%(kappa0_inv))*(kappa_toTv), 2, sum), 10**(-13)))
  return(list(pred_mean=gamma_vec, pred_var=kappa_vec))}
predictGPdevdevdev <-function(fitted_info, t_test, t_tr, f_tr){# obtain the fitted info
  etahat1 <- fitted_info$etahat
  g <- fitted_info$g
  sigmahat <- fitted_info$sigmahat
  gammahat <- fitted_info$gammahat
  
  # obtain the final covariance structure
  
  corr0 <- corr(t_tr, t_tr, etahat1)  # c(t_tr, t_tr)
  kappa0 <- corr0 + g*diag(length(as.vector(f_tr)))
  kappa0_inv <- (1/sigmahat)*solve(kappa0)
  kappa0_inv_f0 <- kappa0_inv%*%(as.vector(f_tr) - gammahat)
  corr_Tv <- corrdevdevdevobv(t_test, t_tr, etahat1)# c(t_test, t_tr)
  kappa_Tv <- sigmahat*corr_Tv# c(t_test, t_tr)
  
  corr_toTv <- corrdevdevdevobv(t_tr, t_test, etahat1)# c(t_tr, t_test)
  kappa_toTv <- sigmahat *corr_toTv#  c(., .)
  
  gamma_vec <-  kappa_Tv%*%kappa0_inv_f0
  dkappa <- sigmahat*(1 + g)*rep(1, dim(t_test)[1]*dim(f_tr)[2])
  kappa_vec <- (pmax(dkappa -apply(t((kappa_Tv)%*%(kappa0_inv))*(kappa_toTv), 2, sum), 10**(-13)))
  return(list(pred_mean=gamma_vec, pred_var=kappa_vec))}
predictGPdevdevdevdev <-function(fitted_info, t_test, t_tr, f_tr){# obtain the fitted info
  etahat1 <- fitted_info$etahat
  g <- fitted_info$g
  sigmahat <- fitted_info$sigmahat
  gammahat <- fitted_info$gammahat
  
  # obtain the final covariance structure
  
  corr0 <- corr(t_tr, t_tr, etahat1)  # c(t_tr, t_tr)
  kappa0 <- corr0 + g*diag(length(as.vector(f_tr)))
  kappa0_inv <- (1/sigmahat)*solve(kappa0)
  kappa0_inv_f0 <- kappa0_inv%*%(as.vector(f_tr) - gammahat)
  corr_Tv <- corrdevdevdevdevobv(t_test, t_tr, etahat1)# c(t_test, t_tr)
  kappa_Tv <- sigmahat*corr_Tv# c(t_test, t_tr)
  
  corr_toTv <- corrdevdevdevdevobv(t_tr, t_test, etahat1)# c(t_tr, t_test)
  kappa_toTv <- sigmahat *corr_toTv#  c(., .)
  
  gamma_vec <-  kappa_Tv%*%kappa0_inv_f0
  dkappa <- sigmahat*(1 + g)*rep(1, dim(t_test)[1]*dim(f_tr)[2])
  kappa_vec <- (pmax(dkappa -apply(t((kappa_Tv)%*%(kappa0_inv))*(kappa_toTv), 2, sum), 10**(-13)))
  return(list(pred_mean=gamma_vec, pred_var=kappa_vec))}
predmeandevdev =rep(0,dim(centercoords)[1])
predLBdevdev =  rep(0,dim(centercoords)[1])
predUBdevdev =rep(0,dim(centercoords)[1])
for(k in 1:dim(centercoords)[1]){
  predinfo <- predictGPdevdev(fitted_info,t(as.matrix(centercoords[k,])), inputtrain, ftrain)
  predmeandevdev[k] <- predinfo$pred_mean
  predLBdevdev[k] = predmeandevdev[k] - qnorm(1-0.05/2)*sqrt(predinfo$pred_var)
  predUBdevdev[k] = predmeandevdev[k]+ qnorm(1-0.05/2)*sqrt(predinfo$pred_var)
}
print(predmeandevdev[inds])
[1]  0.4255432 -0.1365788  0.3426273 -0.4790840  0.1868095
print(predLBdevdev[inds])
[1] -3.365105 -3.459251 -3.072764 -3.648487 -2.956790
print(predUBdevdev[inds])
[1] 4.216191 3.186093 3.758018 2.690319 3.330409
plot(centercoords[,1],predmeandevdev, ylim = c(min(predLBdev),max(predUBdev)))
lines(centercoords[,1],predLBdevdev)
lines(centercoords[,1],predUBdevdev)

predmeandevdevdev =rep(0,dim(centercoords)[1])
predLBdevdevdev =  rep(0,dim(centercoords)[1])
predUBdevdevdev =rep(0,dim(centercoords)[1])
for(k in 1:dim(centercoords)[1]){
  predinfo <- predictGPdevdevdev(fitted_info,t(as.matrix(centercoords[k,])), inputtrain, ftrain)
  predmeandevdevdev[k] <- predinfo$pred_mean
  predLBdevdevdev[k] = predmeandevdevdev[k] - qnorm(1-0.05/2)*sqrt(predinfo$pred_var)
  predUBdevdevdev[k] = predmeandevdevdev[k]+ qnorm(1-0.05/2)*sqrt(predinfo$pred_var)
}
print(predmeandevdevdev[inds])
[1] -0.95180132  0.09850211  0.53404848  0.29814148 -0.26788548
print(predLBdevdevdev[inds])
[1] -9.368393 -7.376385 -7.329279 -6.538623 -6.984487
print(predUBdevdevdev[inds])
[1] 7.464790 7.573389 8.397376 7.134906 6.448717
plot(centercoords[,1],predmeandevdevdev, ylim = c(min(predLBdevdevdev),max(predUBdevdevdev)))
lines(centercoords[,1],predLBdevdevdev)
lines(centercoords[,1],predUBdevdevdev)

predmeandevdevdevdev =rep(0,dim(centercoords)[1])
predLBdevdevdevdev =  rep(0,dim(centercoords)[1])
predUBdevdevdevdev =rep(0,dim(centercoords)[1])
for(k in 1:dim(centercoords)[1]){
  predinfo <- predictGPdevdevdevdev(fitted_info,t(as.matrix(centercoords[k,])), inputtrain, ftrain)
  predmeandevdevdevdev[k] <- predinfo$pred_mean
  predLBdevdevdevdev[k] = predmeandevdevdevdev[k] - qnorm(1-0.05/2)*sqrt(predinfo$pred_var)
  predUBdevdevdevdev[k] = predmeandevdevdevdev[k]+ qnorm(1-0.05/2)*sqrt(predinfo$pred_var)
}
print(predmeandevdevdevdev[inds])
[1] -0.8613916  0.2039218 -0.8864295  0.9720034 -0.2326909
print(predLBdevdevdevdev[inds])
[1] -2.5334432  0.2039211 -0.8864301  0.9720028 -0.2326915
print(predUBdevdevdevdev[inds])
[1]  0.8106600  0.2039224 -0.8864289  0.9720040 -0.2326903
plot(centercoords[,1],predmeandevdevdevdev, ylim = c(min(predLBdevdevdevdev),max(predUBdevdevdevdev)))
lines(centercoords[,1],predLBdevdevdevdev)
lines(centercoords[,1],predUBdevdevdevdev)

kBT = (293*0.001985)
print((exp(predmean[inds[4]]-min(predmean))/kBT)*sqrt(-2*pi*kBT/predmeandevdev[inds[4]]) + kBT*((1/8)*(predmeandevdevdevdev[inds[4]]/(predmeandevdev[inds[4]])^2) - (5/24)*((predmeandevdevdev[inds[4]])^2/(predmeandevdev[inds[4]])^3)))
[1] 24.22749
print((exp(predLB[inds[4]]-min(predLB))/kBT)*sqrt(-2*pi*kBT/predLBdevdev[inds[4]])+ kBT*((1/8)*(predLBdevdevdevdev[inds[4]]/(predLBdevdev[inds[4]])^2) - (5/24)*((predLBdevdevdev[inds[4]])^2/(predLBdevdev[inds[4]])^3)))
[1] 8.784958
ftrain <- as.matrix(FreeE_Propanediol.df[,3])
inputtrain <-as.matrix(FreeE_Propanediol.df[,1:2])
fitted_info <- fitGP(logeta=c(1, 1,1), lowerb=c(0, 0,0), upperb=c(5, 5,5), inputtrain, ftrain)
fitted_info
$etahat
[1] 1 1

$g
[1] 1

$sigmahat
[1] 3.769055

$gammahat
[1] 6.751834
predmean =rep(0,dim(inputtrain)[1])
predLB =  rep(0,dim(inputtrain)[1])
predUB =rep(0,dim(inputtrain)[1])
for(k in 1:dim(inputtrain)[1]){
  predinfo <- predictGP(fitted_info,t(as.matrix(inputtrain[k,])), inputtrain, ftrain)
  predmean[k] <- predinfo$pred_mean
  predLB[k] = predmean[k]- qnorm(1-0.05/2)*sqrt(predinfo$pred_var)
  predUB[k] = predmean[k]+ qnorm(1-0.05/2)*sqrt(predinfo$pred_var)
}
print(paste('PCGPMethod: Test MSE:',round(mean((predmean-ftrain)^2),3),', Coverage:',100*round(mean((predLB<ftrain)*(predUB>ftrain)),3),'%',sep =''))
[1] "PCGPMethod: Test MSE:1.294, Coverage:100%"
FreeE_Propanediol_Pred.df <- FreeE_Propanediol.df
FreeE_Propanediol_LB.df <- FreeE_Propanediol.df
FreeE_Propanediol_UB.df <- FreeE_Propanediol.df
FreeE_Propanediol_Pred.df$freeE <- predmean
FreeE_Propanediol_LB.df$freeE <- predLB
FreeE_Propanediol_UB.df$freeE <- predUB
z <- as.matrix(spread(FreeE_Propanediol.df, `Radial-coord`, freeE)[,-1])
zpred <- as.matrix(spread(FreeE_Propanediol_Pred.df, `Radial-coord`, freeE)[,-1])
zLB <- as.matrix(spread(FreeE_Propanediol_LB.df, `Radial-coord`, freeE)[,-1])
zUB <- as.matrix(spread(FreeE_Propanediol_UB.df, `Radial-coord`, freeE)[,-1])
color <- rep(1, length(z))
dim(color) <- dim(z)
x <-unique(FreeE_Propanediol.df$`Radial-coord`)
y <-unique(FreeE_Propanediol.df$`Axial-coord`)
p <- plot_ly() %>% add_trace( x=x, y=y, z=z,type = "surface",colorscale = list(c(0, 1), c("tan", "blue")))
df1 <- split(FreeE_Propanediol_LB.df, FreeE_Propanediol_LB.df$`Radial-coord`)
df2 <- split(FreeE_Propanediol_LB.df, FreeE_Propanediol_LB.df$`Axial-coord`)
for(i in seq_along(df1)){
  df_sp <- df1[[i]]
  p <- add_trace(p, line = list(
    color = "#000000", 
    width = 2
  ), 
  mode = "lines", 
  type = "scatter3d", 
  x = df_sp$`Radial-coord`,
  y = df_sp$`Axial-coord`,
  z = df_sp$freeE,
  showlegend = FALSE)
}
for(i in seq_along(df2)){
  df_sp <- df2[[i]]
  p <- add_trace(p, line = list(
    color = "#000000", 
    width = 2
  ), 
  mode = "lines", 
  type = "scatter3d", 
  x = df_sp$`Radial-coord`,
  y = df_sp$`Axial-coord`,
  z = df_sp$freeE,
  showlegend = FALSE)
}
df1 <- split(FreeE_Propanediol_UB.df, FreeE_Propanediol_UB.df$`Radial-coord`)
df2 <- split(FreeE_Propanediol_UB.df, FreeE_Propanediol_UB.df$`Axial-coord`)
for(i in seq_along(df1)){
  df_sp <- df1[[i]]
  p <- add_trace(p, line = list(
    color = "#FF0000", 
    width = 2
  ), 
  mode = "lines", 
  type = "scatter3d", 
  x = df_sp$`Radial-coord`,
  y = df_sp$`Axial-coord`,
  z = df_sp$freeE,
  showlegend = FALSE)
}
for(i in seq_along(df2)){
  df_sp <- df2[[i]]
  p <- add_trace(p, line = list(
    color = "#FF0000", 
    width = 2
  ), 
  mode = "lines", 
  type = "scatter3d", 
  x = df_sp$`Radial-coord`,
  y = df_sp$`Axial-coord`,
  z = df_sp$freeE,
  showlegend = FALSE)
}
p%>% layout(scene = list( xaxis = list(title = "Radius, r"),yaxis = list(title = "Axial, z")))
axiallen <- 1000
axialcoord <- unique(FreeE_Propanal.df$`Axial-coord`)
centercoords <-as.matrix( data.frame(seq(min(axialcoord),max(axialcoord),length.out=axiallen),rep(0,axiallen)))
predmean =rep(0,dim(centercoords)[1])
predLB =  rep(0,dim(centercoords)[1])
predUB =rep(0,dim(centercoords)[1])
for(k in 1:dim(centercoords)[1]){
  predinfo <- predictGP(fitted_info,t(as.matrix(centercoords[k,])), inputtrain, ftrain)
  predmean[k] <- predinfo$pred_mean
  predLB[k] = predmean[k]- qnorm(1-0.05/2)*sqrt(predinfo$pred_var)
  predUB[k] = predmean[k]+ qnorm(1-0.05/2)*sqrt(predinfo$pred_var)
}
ind = which(predmean==max(predmean))
print(centercoords[ind,1])
seq.min.axialcoord...max.axialcoord...length.out...axiallen. 
                                                  -0.6891892 
print(predmean[ind])
[1] 6.308108
print(predLB[ind])
[1] 2.846148
print(predUB[ind])
[1] 9.770069
plot(centercoords[,1],predmean, ylim = c(min(predLB),max(predUB)))
lines(centercoords[,1],predLB)
lines(centercoords[,1],predUB)

predmeandev =rep(0,dim(centercoords)[1])
predLBdev =  rep(0,dim(centercoords)[1])
predUBdev =rep(0,dim(centercoords)[1])
for(k in 1:dim(centercoords)[1]){
  predinfo <- predictGPdev(fitted_info,t(as.matrix(centercoords[k,])), inputtrain, ftrain)
  predmeandev[k] <- predinfo$pred_mean
  predLBdev[k] = predmeandev[k] - qnorm(1-0.05/2)*sqrt(predinfo$pred_var)
  predUBdev[k] = predmeandev[k]+ qnorm(1-0.05/2)*sqrt(predinfo$pred_var)
}
inds = which(diff(sign(predmeandev)) != 0)
print(centercoords[inds,1])
[1] -8.0405405 -7.5810811 -5.9134134 -0.6891892  2.1016016  4.4329329  6.9344344
print(predmeandev[inds])
[1] -0.0007317956  0.0033212283 -0.0024386434  0.0037187705 -0.0117369049  0.0007106318 -0.0009734004
print(predLBdev[inds])
[1] -5.698458 -5.618673 -5.702873 -5.641543 -5.709823 -5.620143 -5.704034
print(predUBdev[inds])
[1] 5.696995 5.625315 5.697995 5.648981 5.686349 5.621564 5.702087
plot(centercoords[,1],predmeandev, ylim = c(min(predLBdev),max(predUBdev)))
lines(centercoords[,1],predLBdev)
lines(centercoords[,1],predUBdev)

predmeandevdev =rep(0,dim(centercoords)[1])
predLBdevdev =  rep(0,dim(centercoords)[1])
predUBdevdev =rep(0,dim(centercoords)[1])
for(k in 1:dim(centercoords)[1]){
  predinfo <- predictGPdevdev(fitted_info,t(as.matrix(centercoords[k,])), inputtrain, ftrain)
  predmeandevdev[k] <- predinfo$pred_mean
  predLBdevdev[k] = predmeandevdev[k] - qnorm(1-0.05/2)*sqrt(predinfo$pred_var)
  predUBdevdev[k] = predmeandevdev[k]+ qnorm(1-0.05/2)*sqrt(predinfo$pred_var)
}
print(predmeandevdev[inds])
[1]  0.3513365 -0.2631869  0.1510140 -0.5502032  0.7288531 -0.3181518  0.1565459
print(predLBdevdev[inds])
[1] -4.633672 -4.018359 -4.557604 -4.598919 -3.953395 -4.040190 -4.585034
print(predUBdevdev[inds])
[1] 5.336345 3.491985 4.859632 3.498513 5.411101 3.403887 4.898126
plot(centercoords[,1],predmeandevdev, ylim = c(min(predLBdev),max(predUBdev)))
lines(centercoords[,1],predLBdevdev)
lines(centercoords[,1],predUBdevdev)

predmeandevdevdev =rep(0,dim(centercoords)[1])
predLBdevdevdev =  rep(0,dim(centercoords)[1])
predUBdevdevdev =rep(0,dim(centercoords)[1])
for(k in 1:dim(centercoords)[1]){
  predinfo <- predictGPdevdevdev(fitted_info,t(as.matrix(centercoords[k,])), inputtrain, ftrain)
  predmeandevdevdev[k] <- predinfo$pred_mean
  predLBdevdevdev[k] = predmeandevdevdev[k] - qnorm(1-0.05/2)*sqrt(predinfo$pred_var)
  predUBdevdevdev[k] = predmeandevdevdev[k]+ qnorm(1-0.05/2)*sqrt(predinfo$pred_var)
}
print(predmeandevdevdev[inds])
[1] -1.6050450 -0.7300791 -0.3220568 -0.4499744  0.4405389  0.3292321 -0.3360387
print(predLBdevdevdev[inds])
[1] -12.716097  -7.507184 -11.529364  -8.921627 -10.663563  -6.607474 -11.658531
print(predUBdevdevdev[inds])
[1]  9.506007  6.047025 10.885250  8.021678 11.544641  7.265938 10.986453
plot(centercoords[,1],predmeandevdevdev, ylim = c(min(predLBdevdevdev),max(predUBdevdevdev)))
lines(centercoords[,1],predLBdevdevdev)
lines(centercoords[,1],predUBdevdevdev)

predmeandevdevdevdev =rep(0,dim(centercoords)[1])
predLBdevdevdevdev =  rep(0,dim(centercoords)[1])
predUBdevdevdevdev =rep(0,dim(centercoords)[1])
for(k in 1:dim(centercoords)[1]){
  predinfo <- predictGPdevdevdevdev(fitted_info,t(as.matrix(centercoords[k,])), inputtrain, ftrain)
  predmeandevdevdevdev[k] <- predinfo$pred_mean
  predLBdevdevdevdev[k] = predmeandevdevdevdev[k] - qnorm(1-0.05/2)*sqrt(predinfo$pred_var)
  predUBdevdevdevdev[k] = predmeandevdevdevdev[k]+ qnorm(1-0.05/2)*sqrt(predinfo$pred_var)
}
print(predmeandevdevdevdev[inds])
[1] -0.75730602  3.59103038  0.01582269  1.70411612 -0.96654698 -0.40725528  0.17917950
print(predLBdevdevdevdev[inds])
[1] -4.37970356  3.59102976  0.01582207  1.70411550 -0.96654760 -0.40725590  0.17917888
print(predUBdevdevdevdev[inds])
[1]  2.86509152  3.59103100  0.01582331  1.70411674 -0.96654636 -0.40725466  0.17918012
plot(centercoords[,1],predmeandevdevdevdev, ylim = c(min(predLBdevdevdevdev),max(predUBdevdevdevdev)))
lines(centercoords[,1],predLBdevdevdevdev)
lines(centercoords[,1],predUBdevdevdevdev)

kBT = (293*0.001985)
print((exp(predmean[inds[4]]-min(predmean))/kBT)*sqrt(-2*pi*kBT/predmeandevdev[inds[4]]) + kBT*((1/8)*(predmeandevdevdevdev[inds[4]]/(predmeandevdev[inds[4]])^2) - (5/24)*((predmeandevdevdev[inds[4]])^2/(predmeandevdev[inds[4]])^3)))
[1] 12.20189
print((exp(predLB[inds[4]]-min(predLB))/kBT)*sqrt(-2*pi*kBT/predLBdevdev[inds[4]])+ kBT*((1/8)*(predLBdevdevdevdev[inds[4]]/(predLBdevdev[inds[4]])^2) - (5/24)*((predLBdevdevdev[inds[4]])^2/(predLBdevdev[inds[4]])^3)))
[1] 4.171834
---
title: "R Notebook"
output: html_notebook
---

```{r}
library(readr)
library(taRifx)
library(tidyr)
library(plotly)
```
```{r}
FreeE_Propanediol.df <- read_table2("/home/aarcher/Downloads/FreeE_Propanediol.txt")
FreeE_Propanal.df <- read_table2("/home/aarcher/Downloads/FreeE_Propanal[2].txt")

FreeE_Propanediol.df <- FreeE_Propanediol.df[FreeE_Propanediol.df$`Axial-coord` > -9& FreeE_Propanediol.df$`Axial-coord` < 9,]
FreeE_Propanal.df <- FreeE_Propanal.df[FreeE_Propanal.df$`Axial-coord` > -9& FreeE_Propanal.df$`Axial-coord` < 9,]

FreeE_Propanediol_Center.df <- FreeE_Propanediol.df[FreeE_Propanediol.df$`Radial-coord` == 0.75 & FreeE_Propanediol.df$`Axial-coord` > -9& FreeE_Propanediol.df$`Axial-coord` < 9,]
FreeE_Propanal_Center.df <- FreeE_Propanal.df[FreeE_Propanal.df$`Radial-coord` == 0.75 & FreeE_Propanal.df$`Axial-coord` > -9& FreeE_Propanal.df$`Axial-coord` < 9,]
```

```{r}
ggplot(data = FreeE_Propanediol.df, mapping = aes(x = `Radial-coord`, y = `Axial-coord`, fill = freeE)) + geom_tile() +  xlab(label = "Radius Coord")+  ylab(label = "Axial Coord") + ggtitle('Free Energy Distribution of 1,2-PDO')
plot(FreeE_Propanediol_Center.df$`Axial-coord`,FreeE_Propanediol_Center.df$freeE,ylab='Average Free Energy of 1,2-PDO', xlab='Axial Coord')
```
```{r}
ggplot(data = FreeE_Propanal.df, mapping = aes(x = `Radial-coord`, y = `Axial-coord`, fill = freeE)) + geom_tile() +  xlab(label = "Radius Coord")+  ylab(label = "Axial Coord") + ggtitle('Free Energy Distribution of 1,2-PDO')
plot(FreeE_Propanal_Center.df$`Axial-coord`,FreeE_Propanal_Center.df$freeE,ylab='Average Free Energy of Proponal', xlab='Axial Coord')
```


```{r}
corr <- function(tv1,tv2,eta1){
  K = matrix(1,nrow=dim(tv1)[1],ncol=dim(tv2)[1])
  for(dlcv in 1:dim(tv1)[2]){
  K <- K*exp(-eta1[dlcv]*outer(tv1[,dlcv],tv2[,dlcv],'-')^2)
  }
  K
}



MLE <-function(logeta, to, fo){
  m <- length(logeta)
  logeta1 <- logeta[-m]
  logeta2 <- logeta[m]
  
  # obtain the covariance via kronecker product
  
  corr0 <- corr(to, to, exp(logeta1))# c(., .)
  kappa0 <- corr0 + exp(logeta2)*diag(length(as.vector(fo)))
  kappa0_inv <- solve(kappa0)
  kappa0_inv_f0 <- solve(kappa0, as.vector(fo))
  kappa0_inv_1 <- solve(kappa0, rep(1, length(as.vector(fo))))# estimated values
  gammahat <- sum(kappa0_inv_f0)/sum(kappa0_inv_1)
  sigmahat <- mean(t(kappa0_inv_f0 - gammahat*kappa0_inv_1)*(as.vector(fo) - gammahat))
  return(list(gammahat=gammahat, sigmahat=sigmahat))
  }
```

```{r}
# train each f as GP
negloglik <-function(logeta, t0, f0){
  n <- length(as.vector(f0))# obtain sigmahat for a given eta
  m <- length(logeta)
  logeta1 <- logeta[-m]
  logeta2 <- logeta[m]
  estimators <- MLE(logeta, t0, f0)
  sigmahat <- estimators$sigmahat# obtain the covariance matrices
  corr0 <- corr(t0, t0, exp(logeta1))# c(t0, t0)
  kappa0 <- corr0 + exp(logeta2)*diag(n)

  # obtain the log of determinants efficiently
  logdetkappa0 <- determinant(kappa0,logarithm=TRUE)$modulus
  return(1/2*logdetkappa0 + n/2*log(sigmahat))
  }
```

```{r}
fitGP <-function(logeta=c(1, 1, 1), lowerb=c(-1, -1,-1), upperb=c(4, 4,4), t_tr, f_tr){
  log_eta_hat <- optim(par=logeta,fn=negloglik,lower=lowerb,upper=upperb,method="L-BFGS-B", t0=t_tr, f0=f_tr)$par
  estimators <- MLE(log_eta_hat, t_tr, f_tr)
  m <- length(log_eta_hat)
  return(list(etahat=exp(log_eta_hat[-m]),g=exp(log_eta_hat[m]),sigmahat=estimators$sigmahat,gammahat=estimators$gammahat))
}
predictGP <-function(fitted_info, t_test, t_tr, f_tr){# obtain the fitted info
  etahat1 <- fitted_info$etahat
  g <- fitted_info$g
  sigmahat <- fitted_info$sigmahat
  gammahat <- fitted_info$gammahat
  
  # obtain the final covariance structure
  
  corr0 <- corr(t_tr, t_tr, etahat1)  # c(t_tr, t_tr)
  kappa0 <- corr0 + g*diag(length(as.vector(f_tr)))
  kappa0_inv <- (1/sigmahat)*solve(kappa0)
  kappa0_inv_f0 <- kappa0_inv%*%(as.vector(f_tr) - gammahat)
  corr_Tv <- corr(t_test, t_tr, etahat1)# c(t_test, t_tr)
  kappa_Tv <- sigmahat*corr_Tv# c(t_test, t_tr)
  
  corr_toTv <- corr(t_tr, t_test, etahat1)# c(t_tr, t_test)
  kappa_toTv <- sigmahat *corr_toTv#  c(., .)
  
  gamma_vec <- (gammahat + kappa_Tv%*%kappa0_inv_f0)
  dkappa <- sigmahat * rep(1, dim(t_test)[1]*dim(f_tr)[2])
  kappa_vec <- (pmax(dkappa -apply(t((kappa_Tv)%*%(kappa0_inv))*(kappa_toTv), 2, sum), 10**(-13)))
  return(list(pred_mean=gamma_vec, pred_var=kappa_vec))}
```

```{r}

ftrain <- as.matrix(FreeE_Propanal.df[,3])
inputtrain <-as.matrix(FreeE_Propanal.df[,1:2])
fitted_info <- fitGP(logeta=c(1, 1,1), lowerb=c(0, 0,0), upperb=c(5, 5,5), inputtrain, ftrain)
fitted_info
```


```{r}
predmean =rep(0,dim(inputtrain)[1])
predLB =  rep(0,dim(inputtrain)[1])
predUB =rep(0,dim(inputtrain)[1])
for(k in 1:dim(inputtrain)[1]){
  predinfo <- predictGP(fitted_info,t(as.matrix(inputtrain[k,])), inputtrain, ftrain)
  predmean[k] <- predinfo$pred_mean
  predLB[k] = predmean[k]- qnorm(1-0.05/2)*sqrt(predinfo$pred_var)
  predUB[k] = predmean[k]+ qnorm(1-0.05/2)*sqrt(predinfo$pred_var)
}
print(paste('PCGPMethod: Test MSE:',round(mean((predmean-ftrain)^2),3),', Coverage:',100*round(mean((predLB<ftrain)*(predUB>ftrain)),3),'%',sep =''))
```
```{r}
FreeE_Propanal_Pred.df <- FreeE_Propanal.df
FreeE_Propanal_LB.df <- FreeE_Propanal.df
FreeE_Propanal_UB.df <- FreeE_Propanal.df


FreeE_Propanal_Pred.df$freeE <- predmean
FreeE_Propanal_LB.df$freeE <- predLB
FreeE_Propanal_UB.df$freeE <- predUB
z <- as.matrix(spread(FreeE_Propanal.df, `Radial-coord`, freeE)[,-1])
zpred <- as.matrix(spread(FreeE_Propanal_Pred.df, `Radial-coord`, freeE)[,-1])
zLB <- as.matrix(spread(FreeE_Propanal_LB.df, `Radial-coord`, freeE)[,-1])
zUB <- as.matrix(spread(FreeE_Propanal_UB.df, `Radial-coord`, freeE)[,-1])

color <- rep(1, length(z))
dim(color) <- dim(z)

x <-unique(FreeE_Propanal.df$`Radial-coord`)
y <-unique(FreeE_Propanal.df$`Axial-coord`)

p<-  plot_ly() %>% add_trace(x=FreeE_Propanal.df$`Radial-coord`, y=FreeE_Propanal.df$`Axial-coord`, z=FreeE_Propanal.df$freeE, mode= "markers",type = "scatter3d",marker = list(size = 2, color = "blue", symbol = 104), opacity=0.7,showlegend = FALSE )
p <- p %>% add_trace( x=x, y=y, z=zpred,type = "surface",colorscale = list(c(0, 1), c("tan", "blue")),opacity=0.7)  

df1 <- split(FreeE_Propanal_LB.df, FreeE_Propanal_LB.df$`Radial-coord`)
df2 <- split(FreeE_Propanal_LB.df, FreeE_Propanal_LB.df$`Axial-coord`)

for(i in seq_along(df1)){
  df_sp <- df1[[i]]
  p <- add_trace(p, line = list(
    color = "#000000", 
    width = 2
  ), 
  mode = "lines", 
  type = "scatter3d", 
  x = df_sp$`Radial-coord`,
  y = df_sp$`Axial-coord`,
  z = df_sp$freeE,
  showlegend = FALSE)
}
for(i in seq_along(df2)){
  df_sp <- df2[[i]]
  p <- add_trace(p, line = list(
    color = "#000000", 
    width = 2
  ), 
  mode = "lines", 
  type = "scatter3d", 
  x = df_sp$`Radial-coord`,
  y = df_sp$`Axial-coord`,
  z = df_sp$freeE,
  showlegend = FALSE)
}

df1 <- split(FreeE_Propanal_UB.df, FreeE_Propanal_UB.df$`Radial-coord`)
df2 <- split(FreeE_Propanal_UB.df, FreeE_Propanal_UB.df$`Axial-coord`)

for(i in seq_along(df1)){
  df_sp <- df1[[i]]
  p <- add_trace(p, line = list(
    color = "#FF0000", 
    width = 2
  ), 
  mode = "lines", 
  type = "scatter3d", 
  x = df_sp$`Radial-coord`,
  y = df_sp$`Axial-coord`,
  z = df_sp$freeE,
  showlegend = FALSE)
}
for(i in seq_along(df2)){
  df_sp <- df2[[i]]
  p <- add_trace(p, line = list(
    color = "#FF0000", 
    width = 2
  ), 
  mode = "lines", 
  type = "scatter3d", 
  x = df_sp$`Radial-coord`,
  y = df_sp$`Axial-coord`,
  z = df_sp$freeE,
  showlegend = FALSE)
}
p%>% layout(scene = list( xaxis = list(title = "Radius, r"),yaxis = list(title = "Axial, z")))
```

```{r}

axiallen <- 1000
axialcoord <- unique(FreeE_Propanal.df$`Axial-coord`)
centercoords <-as.matrix( data.frame(seq(min(axialcoord),max(axialcoord),length.out=axiallen),rep(0,axiallen)))

predmean =rep(0,dim(centercoords)[1])
predLB =  rep(0,dim(centercoords)[1])
predUB =rep(0,dim(centercoords)[1])
for(k in 1:dim(centercoords)[1]){
  predinfo <- predictGP(fitted_info,t(as.matrix(centercoords[k,])), inputtrain, ftrain)
  predmean[k] <- predinfo$pred_mean
  predLB[k] = predmean[k]- qnorm(1-0.05/2)*sqrt(predinfo$pred_var)
  predUB[k] = predmean[k]+ qnorm(1-0.05/2)*sqrt(predinfo$pred_var)
}
```

```{r}
plot(centercoords[,1],predmean, ylim = c(min(predLB),max(predUB)))
lines(centercoords[,1],predLB)
lines(centercoords[,1],predUB)
deltax = (max(axialcoord)-min(axialcoord))/(axiallen-1)
predmeandev = (predmean[3:axiallen]-predmean[1:(axiallen-2)])/deltax
preddevLB = (predLB[3:axiallen]-predLB[1:(axiallen-2)])/deltax
preddevUB = (predUB[3:axiallen]-predUB[1:(axiallen-2)])/deltax
predmeandevdev = (predmean[3:axiallen]-2*predmean[2:(axiallen-1)] + predmean[1:(axiallen-2)])/deltax^2
preddevdevLB = (predLB[3:axiallen]-2*predmean[2:(axiallen-1)] +predLB[1:(axiallen-2)])/deltax^2
preddevdevUB = (predUB[3:axiallen]-2*predmean[2:(axiallen-1)] +predUB[1:(axiallen-2)])/deltax^2

indmean = which(predmean==max(predmean))
indLB = which(predLB==max(predLB))
indUB = which(predUB==max(predUB))

print(predmean[indmean])
print(predLB[indLB])
print(predUB[indUB])

plot(centercoords[2:(axiallen-1),1],predmeandev , ylim = c(min(predmeandev,preddevLB,preddevUB),max(predmeandev,preddevLB,preddevUB)))
lines(centercoords[2:(axiallen-1),1],preddevLB)
lines(centercoords[2:(axiallen-1),1],preddevUB)

print(predmeandev[indmean])
print(preddevLB[indLB])
print(preddevUB[indUB])

plot(centercoords[2:(axiallen-1),1],predmeandevdev , ylim = c(min(predmeandevdev,preddevdevLB,preddevdevUB),max(predmeandevdev,preddevdevLB,preddevdevUB)))
lines(centercoords[2:(axiallen-1),1],preddevdevLB)
lines(centercoords[2:(axiallen-1),1],preddevdevUB)

print(predmeandevdev[indmean])
print(preddevdevLB[indLB])
print(preddevdevUB[indUB])


```

```{r}
corrdevobv <- function(tv1,tv2,eta1){
  K <- -2*eta1[1]*exp(-eta1[1]*outer(tv1[,1],tv2[,1],'-')^2)*(outer(tv1[,1],tv2[,1],'-'))
  K <- K*exp(-eta1[2]*abs(outer(tv1[,2],tv2[,2],'-'))^2)
  K
}

predictGPdev <-function(fitted_info, t_test, t_tr, f_tr){# obtain the fitted info
  etahat1 <- fitted_info$etahat
  g <- fitted_info$g
  sigmahat <- fitted_info$sigmahat
  gammahat <- fitted_info$gammahat
  
  # obtain the final covariance structure
  
  corr0 <- corr(t_tr, t_tr, etahat1)  # c(t_tr, t_tr)
  kappa0 <- corr0 + g*diag(length(as.vector(f_tr)))
  kappa0_inv <- (1/sigmahat)*solve(kappa0)
  kappa0_inv_f0 <- kappa0_inv%*%(as.vector(f_tr) - gammahat)
  corr_Tv <- corrdevobv(t_test, t_tr, etahat1)# c(t_test, t_tr)
  kappa_Tv <- sigmahat*corr_Tv# c(t_test, t_tr)
  
  corr_toTv <- corrdevobv(t_tr, t_test, etahat1)# c(t_tr, t_test)
  kappa_toTv <- sigmahat *corr_toTv#  c(., .)
  
  gamma_vec <-  kappa_Tv%*%kappa0_inv_f0
  dkappa <- sigmahat*(1 + g)*rep(1, dim(t_test)[1]*dim(f_tr)[2])
  kappa_vec <- (pmax(dkappa -apply(t((kappa_Tv)%*%(kappa0_inv))*(kappa_toTv), 2, sum), 10**(-13)))
  return(list(pred_mean=gamma_vec, pred_var=kappa_vec))}
```

```{r}

predmeandev =rep(0,dim(centercoords)[1])
predLBdev =  rep(0,dim(centercoords)[1])
predUBdev =rep(0,dim(centercoords)[1])
for(k in 1:dim(centercoords)[1]){
  predinfo <- predictGPdev(fitted_info,t(as.matrix(centercoords[k,])), inputtrain, ftrain)
  predmeandev[k] <- predinfo$pred_mean
  predLBdev[k] = predmeandev[k] - qnorm(1-0.05/2)*sqrt(predinfo$pred_var)
  predUBdev[k] = predmeandev[k]+ qnorm(1-0.05/2)*sqrt(predinfo$pred_var)
}
```


```{r}
plot(centercoords[,1],predmeandev)# ylim = c(min(predLBdev),max(predUBdev)))
lines(centercoords[,1],predLBdev)
lines(centercoords[,1],predUBdev)
inds = which(diff(sign(predmeandev)) != 0)
print(predmeandev[inds])
print(predLBdev[inds])
print(predUBdev[inds])
```

```{r}
corrdevdevobv <- function(tv1,tv2,eta1){
  K <- 2*eta1[1]*exp(-eta1[1]*outer(tv1[,1],tv2[,1],'-')^2)*(2*eta1[1]*(outer(tv1[,1],tv2[,1],'-'))^2-1)
  K <- K*exp(-eta1[2]*abs(outer(tv1[,2],tv2[,2],'-'))^2)
  K
}

corrdevdevdevobv <- function(tv1,tv2,eta1){
  K <- -4*(eta1[1]^2)*(outer(tv1[,1],tv2[,1],'-'))*exp(-eta1[1]*outer(tv1[,1],tv2[,1],'-')^2)*(2*eta1[1]*(outer(tv1[,1],tv2[,1],'-'))^2-3)
  K <- K*exp(-eta1[2]*abs(outer(tv1[,2],tv2[,2],'-'))^2)
  K
}

corrdevdevdevdevobv <- function(tv1,tv2,eta1){
  K <- 4*(eta1[1]^2)*exp(-eta1[1]*outer(tv1[,1],tv2[,1],'-')^2)*(4*eta1[1]*(outer(tv1[,1],tv2[,1],'-')^2)*(eta1[1]*(outer(tv1[,1],tv2[,1],'-'))^2-3)+3)
  K <- K*exp(-eta1[2]*abs(outer(tv1[,2],tv2[,2],'-'))^2)
  K
}

predictGPdevdev <-function(fitted_info, t_test, t_tr, f_tr){# obtain the fitted info
  etahat1 <- fitted_info$etahat
  g <- fitted_info$g
  sigmahat <- fitted_info$sigmahat
  gammahat <- fitted_info$gammahat
  
  # obtain the final covariance structure
  
  corr0 <- corr(t_tr, t_tr, etahat1)  # c(t_tr, t_tr)
  kappa0 <- corr0 + g*diag(length(as.vector(f_tr)))
  kappa0_inv <- (1/sigmahat)*solve(kappa0)
  kappa0_inv_f0 <- kappa0_inv%*%(as.vector(f_tr) - gammahat)
  corr_Tv <- corrdevdevobv(t_test, t_tr, etahat1)# c(t_test, t_tr)
  kappa_Tv <- sigmahat*corr_Tv# c(t_test, t_tr)
  
  corr_toTv <- corrdevdevobv(t_tr, t_test, etahat1)# c(t_tr, t_test)
  kappa_toTv <- sigmahat *corr_toTv#  c(., .)
  
  gamma_vec <-  kappa_Tv%*%kappa0_inv_f0
  dkappa <- sigmahat*(1 + g)*rep(1, dim(t_test)[1]*dim(f_tr)[2])
  kappa_vec <- (pmax(dkappa -apply(t((kappa_Tv)%*%(kappa0_inv))*(kappa_toTv), 2, sum), 10**(-13)))
  return(list(pred_mean=gamma_vec, pred_var=kappa_vec))}

predictGPdevdevdev <-function(fitted_info, t_test, t_tr, f_tr){# obtain the fitted info
  etahat1 <- fitted_info$etahat
  g <- fitted_info$g
  sigmahat <- fitted_info$sigmahat
  gammahat <- fitted_info$gammahat
  
  # obtain the final covariance structure
  
  corr0 <- corr(t_tr, t_tr, etahat1)  # c(t_tr, t_tr)
  kappa0 <- corr0 + g*diag(length(as.vector(f_tr)))
  kappa0_inv <- (1/sigmahat)*solve(kappa0)
  kappa0_inv_f0 <- kappa0_inv%*%(as.vector(f_tr) - gammahat)
  corr_Tv <- corrdevdevdevobv(t_test, t_tr, etahat1)# c(t_test, t_tr)
  kappa_Tv <- sigmahat*corr_Tv# c(t_test, t_tr)
  
  corr_toTv <- corrdevdevdevobv(t_tr, t_test, etahat1)# c(t_tr, t_test)
  kappa_toTv <- sigmahat *corr_toTv#  c(., .)
  
  gamma_vec <-  kappa_Tv%*%kappa0_inv_f0
  dkappa <- sigmahat*(1 + g)*rep(1, dim(t_test)[1]*dim(f_tr)[2])
  kappa_vec <- (pmax(dkappa -apply(t((kappa_Tv)%*%(kappa0_inv))*(kappa_toTv), 2, sum), 10**(-13)))
  return(list(pred_mean=gamma_vec, pred_var=kappa_vec))}

predictGPdevdevdevdev <-function(fitted_info, t_test, t_tr, f_tr){# obtain the fitted info
  etahat1 <- fitted_info$etahat
  g <- fitted_info$g
  sigmahat <- fitted_info$sigmahat
  gammahat <- fitted_info$gammahat
  
  # obtain the final covariance structure
  
  corr0 <- corr(t_tr, t_tr, etahat1)  # c(t_tr, t_tr)
  kappa0 <- corr0 + g*diag(length(as.vector(f_tr)))
  kappa0_inv <- (1/sigmahat)*solve(kappa0)
  kappa0_inv_f0 <- kappa0_inv%*%(as.vector(f_tr) - gammahat)
  corr_Tv <- corrdevdevdevdevobv(t_test, t_tr, etahat1)# c(t_test, t_tr)
  kappa_Tv <- sigmahat*corr_Tv# c(t_test, t_tr)
  
  corr_toTv <- corrdevdevdevdevobv(t_tr, t_test, etahat1)# c(t_tr, t_test)
  kappa_toTv <- sigmahat *corr_toTv#  c(., .)
  
  gamma_vec <-  kappa_Tv%*%kappa0_inv_f0
  dkappa <- sigmahat*(1 + g)*rep(1, dim(t_test)[1]*dim(f_tr)[2])
  kappa_vec <- (pmax(dkappa -apply(t((kappa_Tv)%*%(kappa0_inv))*(kappa_toTv), 2, sum), 10**(-13)))
  return(list(pred_mean=gamma_vec, pred_var=kappa_vec))}
```

```{r}

predmeandevdev =rep(0,dim(centercoords)[1])
predLBdevdev =  rep(0,dim(centercoords)[1])
predUBdevdev =rep(0,dim(centercoords)[1])
for(k in 1:dim(centercoords)[1]){
  predinfo <- predictGPdevdev(fitted_info,t(as.matrix(centercoords[k,])), inputtrain, ftrain)
  predmeandevdev[k] <- predinfo$pred_mean
  predLBdevdev[k] = predmeandevdev[k] - qnorm(1-0.05/2)*sqrt(predinfo$pred_var)
  predUBdevdev[k] = predmeandevdev[k]+ qnorm(1-0.05/2)*sqrt(predinfo$pred_var)
}
print(predmeandevdev[inds])
print(predLBdevdev[inds])
print(predUBdevdev[inds])
```


```{r}
plot(centercoords[,1],predmeandevdev, ylim = c(min(predLBdev),max(predUBdev)))
lines(centercoords[,1],predLBdevdev)
lines(centercoords[,1],predUBdevdev)
```

```{r}

predmeandevdevdev =rep(0,dim(centercoords)[1])
predLBdevdevdev =  rep(0,dim(centercoords)[1])
predUBdevdevdev =rep(0,dim(centercoords)[1])
for(k in 1:dim(centercoords)[1]){
  predinfo <- predictGPdevdevdev(fitted_info,t(as.matrix(centercoords[k,])), inputtrain, ftrain)
  predmeandevdevdev[k] <- predinfo$pred_mean
  predLBdevdevdev[k] = predmeandevdevdev[k] - qnorm(1-0.05/2)*sqrt(predinfo$pred_var)
  predUBdevdevdev[k] = predmeandevdevdev[k]+ qnorm(1-0.05/2)*sqrt(predinfo$pred_var)
}
print(predmeandevdevdev[inds])
print(predLBdevdevdev[inds])
print(predUBdevdevdev[inds])
```


```{r}
plot(centercoords[,1],predmeandevdevdev, ylim = c(min(predLBdevdevdev),max(predUBdevdevdev)))
lines(centercoords[,1],predLBdevdevdev)
lines(centercoords[,1],predUBdevdevdev)
```

```{r}

predmeandevdevdevdev =rep(0,dim(centercoords)[1])
predLBdevdevdevdev =  rep(0,dim(centercoords)[1])
predUBdevdevdevdev =rep(0,dim(centercoords)[1])
for(k in 1:dim(centercoords)[1]){
  predinfo <- predictGPdevdevdevdev(fitted_info,t(as.matrix(centercoords[k,])), inputtrain, ftrain)
  predmeandevdevdevdev[k] <- predinfo$pred_mean
  predLBdevdevdevdev[k] = predmeandevdevdevdev[k] - qnorm(1-0.05/2)*sqrt(predinfo$pred_var)
  predUBdevdevdevdev[k] = predmeandevdevdevdev[k]+ qnorm(1-0.05/2)*sqrt(predinfo$pred_var)
}
print(predmeandevdevdevdev[inds])
print(predLBdevdevdevdev[inds])
print(predUBdevdevdevdev[inds])
```


```{r}
plot(centercoords[,1],predmeandevdevdevdev, ylim = c(min(predLBdevdevdevdev),max(predUBdevdevdevdev)))
lines(centercoords[,1],predLBdevdevdevdev)
lines(centercoords[,1],predUBdevdevdevdev)
```

```{r}
kBT = (293*0.001985)
print((exp(predmean[inds[4]]-min(predmean))/kBT)*sqrt(-2*pi*kBT/predmeandevdev[inds[4]]) + kBT*((1/8)*(predmeandevdevdevdev[inds[4]]/(predmeandevdev[inds[4]])^2) - (5/24)*((predmeandevdevdev[inds[4]])^2/(predmeandevdev[inds[4]])^3)))
print((exp(predLB[inds[4]]-min(predLB))/kBT)*sqrt(-2*pi*kBT/predLBdevdev[inds[4]])+ kBT*((1/8)*(predLBdevdevdevdev[inds[4]]/(predLBdevdev[inds[4]])^2) - (5/24)*((predLBdevdevdev[inds[4]])^2/(predLBdevdev[inds[4]])^3)))

```

```{r}
ftrain <- as.matrix(FreeE_Propanediol.df[,3])
inputtrain <-as.matrix(FreeE_Propanediol.df[,1:2])
fitted_info <- fitGP(logeta=c(1, 1,1), lowerb=c(0, 0,0), upperb=c(5, 5,5), inputtrain, ftrain)
fitted_info
```


```{r}
predmean =rep(0,dim(inputtrain)[1])
predLB =  rep(0,dim(inputtrain)[1])
predUB =rep(0,dim(inputtrain)[1])
for(k in 1:dim(inputtrain)[1]){
  predinfo <- predictGP(fitted_info,t(as.matrix(inputtrain[k,])), inputtrain, ftrain)
  predmean[k] <- predinfo$pred_mean
  predLB[k] = predmean[k]- qnorm(1-0.05/2)*sqrt(predinfo$pred_var)
  predUB[k] = predmean[k]+ qnorm(1-0.05/2)*sqrt(predinfo$pred_var)
}
print(paste('PCGPMethod: Test MSE:',round(mean((predmean-ftrain)^2),3),', Coverage:',100*round(mean((predLB<ftrain)*(predUB>ftrain)),3),'%',sep =''))
```
```{r}
FreeE_Propanediol_Pred.df <- FreeE_Propanediol.df
FreeE_Propanediol_LB.df <- FreeE_Propanediol.df
FreeE_Propanediol_UB.df <- FreeE_Propanediol.df


FreeE_Propanediol_Pred.df$freeE <- predmean
FreeE_Propanediol_LB.df$freeE <- predLB
FreeE_Propanediol_UB.df$freeE <- predUB

z <- as.matrix(spread(FreeE_Propanediol.df, `Radial-coord`, freeE)[,-1])
zpred <- as.matrix(spread(FreeE_Propanediol_Pred.df, `Radial-coord`, freeE)[,-1])
zLB <- as.matrix(spread(FreeE_Propanediol_LB.df, `Radial-coord`, freeE)[,-1])
zUB <- as.matrix(spread(FreeE_Propanediol_UB.df, `Radial-coord`, freeE)[,-1])

color <- rep(1, length(z))
dim(color) <- dim(z)

x <-unique(FreeE_Propanediol.df$`Radial-coord`)
y <-unique(FreeE_Propanediol.df$`Axial-coord`)
p <- plot_ly() %>% add_trace( x=x, y=y, z=z,type = "surface",colorscale = list(c(0, 1), c("tan", "blue")))

df1 <- split(FreeE_Propanediol_LB.df, FreeE_Propanediol_LB.df$`Radial-coord`)
df2 <- split(FreeE_Propanediol_LB.df, FreeE_Propanediol_LB.df$`Axial-coord`)

for(i in seq_along(df1)){
  df_sp <- df1[[i]]
  p <- add_trace(p, line = list(
    color = "#000000", 
    width = 2
  ), 
  mode = "lines", 
  type = "scatter3d", 
  x = df_sp$`Radial-coord`,
  y = df_sp$`Axial-coord`,
  z = df_sp$freeE,
  showlegend = FALSE)
}
for(i in seq_along(df2)){
  df_sp <- df2[[i]]
  p <- add_trace(p, line = list(
    color = "#000000", 
    width = 2
  ), 
  mode = "lines", 
  type = "scatter3d", 
  x = df_sp$`Radial-coord`,
  y = df_sp$`Axial-coord`,
  z = df_sp$freeE,
  showlegend = FALSE)
}

df1 <- split(FreeE_Propanediol_UB.df, FreeE_Propanediol_UB.df$`Radial-coord`)
df2 <- split(FreeE_Propanediol_UB.df, FreeE_Propanediol_UB.df$`Axial-coord`)

for(i in seq_along(df1)){
  df_sp <- df1[[i]]
  p <- add_trace(p, line = list(
    color = "#FF0000", 
    width = 2
  ), 
  mode = "lines", 
  type = "scatter3d", 
  x = df_sp$`Radial-coord`,
  y = df_sp$`Axial-coord`,
  z = df_sp$freeE,
  showlegend = FALSE)
}
for(i in seq_along(df2)){
  df_sp <- df2[[i]]
  p <- add_trace(p, line = list(
    color = "#FF0000", 
    width = 2
  ), 
  mode = "lines", 
  type = "scatter3d", 
  x = df_sp$`Radial-coord`,
  y = df_sp$`Axial-coord`,
  z = df_sp$freeE,
  showlegend = FALSE)
}
p%>% layout(scene = list( xaxis = list(title = "Radius, r"),yaxis = list(title = "Axial, z")))
```

```{r}


axiallen <- 1000
axialcoord <- unique(FreeE_Propanal.df$`Axial-coord`)
centercoords <-as.matrix( data.frame(seq(min(axialcoord),max(axialcoord),length.out=axiallen),rep(0,axiallen)))

predmean =rep(0,dim(centercoords)[1])
predLB =  rep(0,dim(centercoords)[1])
predUB =rep(0,dim(centercoords)[1])
for(k in 1:dim(centercoords)[1]){
  predinfo <- predictGP(fitted_info,t(as.matrix(centercoords[k,])), inputtrain, ftrain)
  predmean[k] <- predinfo$pred_mean
  predLB[k] = predmean[k]- qnorm(1-0.05/2)*sqrt(predinfo$pred_var)
  predUB[k] = predmean[k]+ qnorm(1-0.05/2)*sqrt(predinfo$pred_var)
}
ind = which(predmean==max(predmean))
print(centercoords[ind,1])
print(predmean[ind])
print(predLB[ind])
print(predUB[ind])
```

```{r}
plot(centercoords[,1],predmean, ylim = c(min(predLB),max(predUB)))
lines(centercoords[,1],predLB)
lines(centercoords[,1],predUB)

```

```{r}

predmeandev =rep(0,dim(centercoords)[1])
predLBdev =  rep(0,dim(centercoords)[1])
predUBdev =rep(0,dim(centercoords)[1])
for(k in 1:dim(centercoords)[1]){
  predinfo <- predictGPdev(fitted_info,t(as.matrix(centercoords[k,])), inputtrain, ftrain)
  predmeandev[k] <- predinfo$pred_mean
  predLBdev[k] = predmeandev[k] - qnorm(1-0.05/2)*sqrt(predinfo$pred_var)
  predUBdev[k] = predmeandev[k]+ qnorm(1-0.05/2)*sqrt(predinfo$pred_var)
}
inds = which(diff(sign(predmeandev)) != 0)
print(centercoords[inds,1])

print(predmeandev[inds])
print(predLBdev[inds])
print(predUBdev[inds])
```


```{r}
plot(centercoords[,1],predmeandev, ylim = c(min(predLBdev),max(predUBdev)))
lines(centercoords[,1],predLBdev)
lines(centercoords[,1],predUBdev)

```

```{r}

predmeandevdev =rep(0,dim(centercoords)[1])
predLBdevdev =  rep(0,dim(centercoords)[1])
predUBdevdev =rep(0,dim(centercoords)[1])
for(k in 1:dim(centercoords)[1]){
  predinfo <- predictGPdevdev(fitted_info,t(as.matrix(centercoords[k,])), inputtrain, ftrain)
  predmeandevdev[k] <- predinfo$pred_mean
  predLBdevdev[k] = predmeandevdev[k] - qnorm(1-0.05/2)*sqrt(predinfo$pred_var)
  predUBdevdev[k] = predmeandevdev[k]+ qnorm(1-0.05/2)*sqrt(predinfo$pred_var)
}
print(predmeandevdev[inds])
print(predLBdevdev[inds])
print(predUBdevdev[inds])
```


```{r}
plot(centercoords[,1],predmeandevdev, ylim = c(min(predLBdev),max(predUBdev)))
lines(centercoords[,1],predLBdevdev)
lines(centercoords[,1],predUBdevdev)
```

```{r}

predmeandevdevdev =rep(0,dim(centercoords)[1])
predLBdevdevdev =  rep(0,dim(centercoords)[1])
predUBdevdevdev =rep(0,dim(centercoords)[1])
for(k in 1:dim(centercoords)[1]){
  predinfo <- predictGPdevdevdev(fitted_info,t(as.matrix(centercoords[k,])), inputtrain, ftrain)
  predmeandevdevdev[k] <- predinfo$pred_mean
  predLBdevdevdev[k] = predmeandevdevdev[k] - qnorm(1-0.05/2)*sqrt(predinfo$pred_var)
  predUBdevdevdev[k] = predmeandevdevdev[k]+ qnorm(1-0.05/2)*sqrt(predinfo$pred_var)
}
print(predmeandevdevdev[inds])
print(predLBdevdevdev[inds])
print(predUBdevdevdev[inds])
```


```{r}
plot(centercoords[,1],predmeandevdevdev, ylim = c(min(predLBdevdevdev),max(predUBdevdevdev)))
lines(centercoords[,1],predLBdevdevdev)
lines(centercoords[,1],predUBdevdevdev)
```

```{r}

predmeandevdevdevdev =rep(0,dim(centercoords)[1])
predLBdevdevdevdev =  rep(0,dim(centercoords)[1])
predUBdevdevdevdev =rep(0,dim(centercoords)[1])
for(k in 1:dim(centercoords)[1]){
  predinfo <- predictGPdevdevdevdev(fitted_info,t(as.matrix(centercoords[k,])), inputtrain, ftrain)
  predmeandevdevdevdev[k] <- predinfo$pred_mean
  predLBdevdevdevdev[k] = predmeandevdevdevdev[k] - qnorm(1-0.05/2)*sqrt(predinfo$pred_var)
  predUBdevdevdevdev[k] = predmeandevdevdevdev[k]+ qnorm(1-0.05/2)*sqrt(predinfo$pred_var)
}
print(predmeandevdevdevdev[inds])
print(predLBdevdevdevdev[inds])
print(predUBdevdevdevdev[inds])
```


```{r}
plot(centercoords[,1],predmeandevdevdevdev, ylim = c(min(predLBdevdevdevdev),max(predUBdevdevdevdev)))
lines(centercoords[,1],predLBdevdevdevdev)
lines(centercoords[,1],predUBdevdevdevdev)
```

```{r}
kBT = (293*0.001985)
print((exp(predmean[inds[4]]-min(predmean))/kBT)*sqrt(-2*pi*kBT/predmeandevdev[inds[4]]) + kBT*((1/8)*(predmeandevdevdevdev[inds[4]]/(predmeandevdev[inds[4]])^2) - (5/24)*((predmeandevdevdev[inds[4]])^2/(predmeandevdev[inds[4]])^3)))
print((exp(predLB[inds[4]]-min(predLB))/kBT)*sqrt(-2*pi*kBT/predLBdevdev[inds[4]])+ kBT*((1/8)*(predLBdevdevdevdev[inds[4]]/(predLBdevdev[inds[4]])^2) - (5/24)*((predLBdevdevdev[inds[4]])^2/(predLBdevdev[inds[4]])^3)))

```